Intermediate Algebra (11th edition)

Solving an Equation for One of the Variables

Solve the equation for y.

Our goal is to isolate yon one side of the equation.

Subtract 3x.

Combine like terms.

Divide by

There are other equivalent forms of the final answer that are also

correct. For example, since (Section 1.2),we rewrite the

fraction by moving the negative sign from the denominator to the

numerator, taking care to distribute to both terms.

can be written as or y=

3 x- 12

4

y=.

- 112 - 3 x 2

4

y= ,

12 - 3 x

- 4

a

- b=

• a
  b

y=

12 - 3 x

- 4

- 4.

- 4 y

- 4

=

12 - 3 x

- 4

- 4 y= 12 - 3 x

3 x- 4 y- 3 x= 12 - 3 x

3 x- 4 y= 12

3 x- 4 y= 12

EXAMPLE 4

SECTION 2.2 Formulas and Percent 59

NOW TRY
EXERCISE 4
Solve the equation for y.

5 x- 6 y= 12

NOW TRY ANSWERS

4. y=^12 - - 65 x , or y=^5 x 6 -^12

NOW TRY

OBJECTIVE 2 Solve applied problems by using formulas. The distance for-

mula, relates d, the distance traveled, r, the rate or speed, and t, the travel time.

Finding Average Rate

Phyllis Koenig found that on average it took her each day to drive a distance of

15 mi to work. What was her average rate (or speed)?

Find the formula for rate rby solving for r.

Divide by t.

or

Notice that only Step 3 was needed to solve for rin this example. Now find the rate

by substituting the given values of dand tinto this formula.

Let

Multiply by the reciprocal of

Her average rate was 20 mph. (That is, at times she may have traveled a little faster or

slower than 20 mph, but overall her rate was 20 mph.) NOW TRY

r= 20

3

r= 15 # 4.

4

3

d=15, t=^34.

15

3

4

r=

r=

d

t

d

t

=r,

d

t

=

rt

t

d=rt

d=rt

3

4 hr

EXAMPLE 5

d= rt,

NOW TRY

EXERCISE 5

It takes hr for Dorothy
Easley to drive 21 mi to work
each day. What is her average
rate?

1

2

5. 42 mph

Multiply both terms

of the numerator

by 1.-